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(For updated locations, see the timetable; All locations are subject to change) AMS Short CoursesRegistrationTwo Short Course proposals have been selected for presentation just before the Joint Mathematics Meetings begin. These Short Courses will take place on January 2 and 3, 2012 (Monday and Tuesday), Sheraton Boston. Topics will be Random Fields and Random Geometry and Computing with Elliptic Curves using Sage. The cost to participate is the same for both courses. Advance registration fees are: member of the AMS or MAA, US$102; nonmembers are US$145; students, unemployed, or emeritus are US$50. These fees are in effect until December 15. If you choose to register at the meeting, the fees are US$136 for members of the AMS or MAA, US$175 for nonmembers, and US$71 for students, unemployed, or emeritus. Advance registration will begin on September 1, 2011. Onsite registration will take place on Monday, January 2, 2012, 8:00 a.m.  noon, Back Bay Ballroom D, Sheraton. Random Fields and Random Geometry
Location: Back Bay Ballroom A, 2nd Floor, Sheraton IntroductionThe main theme of the lectures will be to describe the geometric aspects of smooth Gaussian and related random processes over parameter spaces of dimension 2 and higher. The study of such processes known as random fields  has seen significant theoretical advances over the past decade. While these developments have occurred primarily with the framework of Probability and Stochastic Geometry, the new results and techniques are feeding ideas back into the mathematical world of topology and are finding new applications in areas which have traditionally used random fields as stochastic models. Among these are:
The lectures and tutorials of this short course will be designed to give a broad introduction to the modern theory of smooth random fields as well as describing some of its more exciting and important applications. LecturesWe have the following confirmed speakers with preliminary titles and abstracts for their talks.
Gaussian Fields and KacRice formulae Course Materials Lecture notes can be found here.
The Gaussian kinematic formula Course Materials Lecture notes can be found here.
Random matrices and Gaussian analytic functions
Gaussian models in fMRI image analysis Course Materials The slides can be found at http://webee.technion.ac.il/people/adler/jonathan2boston.pdf.
Random fields in physics Course Materials Lecture notes can be found here.
Random metrics Course Materials Lecture notes can be found here. The slides can be found at http://webee.technion.ac.il/people/adler/dimaboston.pdf. ScheduleIt is planned that each lecture will be 75 minutes long. There will be two lectures each morning and one following lunch. On the first day the remainder of the afternoon will be devoted to tutorial sessions aimed at getting hands on experience with the basic results of Gaussian random field theory. On the second day there will be discussion groups on each of the application areas treated in the main lectures. Computing with Elliptic Curves Using Sage
Location: Back Bay Ballroom B, 2nd Floor, Sheraton Course MaterialsA current snapshot of the Sage worksheets, slides, etc. for the short course on elliptic curves can be found at http://wiki.sagemath.org/jmm12?action=AttachFile&do=get&target=JMM2011notes.pdf Links to individual course materials such as Sage worksheets under Course Materials can be found at http://wiki.sagemath.org/jmm12 . 1 IntroductionThis short course will explore computing with elliptic curves using the free open source mathematical software system Sage. Half of the lectures will be accessible to a general mathematical audience with little prior exposure to elliptic curves, and will provide a good way for mathematicians to learn about Sage in the context of strikingly beautiful mathematics.
An elliptic curve is a curve defined by a cubic equation of the form y2 = x3 + Ax + B in two variables x and y. The extent to which elliptic curves play a central role in both pure and applied modern number theory is astounding. Deep problems in number theory such as the congruent number problemwhich integers are the area of a right triangle with rational side lengths?translate naturally into questions about elliptic curves. Other questions, such as the famous unsolved Birch and SwinnertonDyer conjecture, propose startling relationships between algebra and analysis. Elliptic curves also play a starring role in Andrew Wiles's proof of Fermat's Last Theorem by arising naturally from any counterexample to the assertion. In a more applied direction, the abelian groups attached to elliptic curves over finite fields are extremely advantageous in the construction of publickey cryptosystems. In particular, elliptic curves are widely believed to provide good security with small key sizes, which is useful in applicationsif we are going to print an encryption key on a postage stamp, it is helpful if the key is short! Sage (see http://sagemath.org) is a free opensource mathematics software system licensed under the GNU Public License. It has extensive capabilities for computing with elliptic curves. Sage is built out of around 100 opensource packages and features a unifed interface. Sage can be used to study elementary and advanced, pure and applied mathematics. This includes a huge range of mathematics, including basic algebra, calculus, elementary to advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more. It combines various software packages and seamlessly integrates their functionality into a common experience. It is well suited for education and research. The user interface is a notebook in a web browser or the command line. Using the notebook, Sage connects either locally to your own Sage installation or to a Sage server on the network. Inside the Sage notebook you can create embedded graphics, beautifully typeset mathematical expressions, add and delete input, and share your work across the network. Topics covered in the course may include:
2 Lecture Series2.1 Introduction to Python and Sage Kiran Kedlaya, UC San Diego Kedlaya will give an overview of how to use Sage using the Python programming language. No prior knowledge of Python or Sage will be assumed. 2.2 Computing with elliptic curves over finite fields using Sage Ken Ribet, UC Berkeley Ribet will explain how to use Sage to perform the sort of computations with elliptic curves over finite fields that are needed to follow along with a cryptography book and do exercises that involve long computations. 2.3 Computing with elliptic surfaces Noam Elkies, Harvard University Elkies's lectures will link some of the same arithmetical ideas that appear in the other lectures with other mathematical topics including algebraic geometry of surfaces, Euclidean and hyperbolic lattices, etc., that either are already or should be in Sage. This topic will also touch on elliptic curves of high rank, since every rank record is obtained by specialization from an elliptic surface (or possibly an elliptic curve over P^n for some n > 1). 2.4 Computing with ShafarevichTate Groups using Sage Jared Weinstein, Boston University The ShafarevichTate group is the most mysterious invariant attached to an elliptic curve. Weinstein will explain how to use Sage to compute information about ShafarevichTate groups. His talk may touch on work of Heegner, Kolvyagin, Kato, Schneider, Mazur and others. 2.5 Using Sage to explore the Birch and SwinnertonDyer conjecture William Stein, University of Washington Stein will introduce the Birch and SwinnertonDyer conjecture via the congruent number problem. He will then discuss how to use Sage to compute MordellWeil groups, values of Lfunctions, regulators, heights, and Tamagawa numbers. He will also talk about computing the Birch and SwinnertonDyer invariants for various tables of elliptic curves. 
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